1. For a triangle to be a right triangle, it must satisfy the Pythagorean theorem: [tex]a^2=b^2+c^2[/tex]; the square of the longest side (hypotenuse) of the triangle is equal to the sum of the squares of its shorter sides.
We know from our problem that the longest side of our triangle is 15 cm long and the shorter sides are 13 cm and 14 cm respectively, so:
[tex]a^2=b^2+c^2[/tex]
[tex]15^2=13^2+14^2
[/tex]
[tex]225=169+196[/tex]
[tex]225 \neq 365[/tex]
We can conclude that the triangle
is NOT a right triangle.
2. Just as before, for a triangle to be a right triangle, it must satisfy the Pythagorean theorem: [tex]a^2=b^2+c^2[/tex]; the square of the longest side (hypotenuse) of the triangle is equal to the sum of the squares of its shorter sides.
We know from our triangle that its longest side is 8 ft long and its shorter sides are 4,8 ft and 6.4 ft, so lets use the Pythagorean theorem:
[tex]a^2=b^2+c^2[/tex]
[tex]8^2=4.8^2+6.4^2[/tex]
[tex]64=23.04+40.96[/tex]
[tex]64=64[/tex]
We can conclude that the triangle
IS a right triangle.
3. They used a rope with
12 evenly spaced knots to represent a measure of 12 units, then, they used a
section of the rope of 3 knots to represent one of the legs of a triangle and
another section of 4 knots to represent the other one. Then they used the
rest of the rope (5 knots) to join the two legs of the triangle. Therefore,
they formed a triangle with 5 knots as its longest side and 4 and 3 knots as
its shorter sides.
Lets cheek if that triangle satisfies the Pythagorean theorem:
[tex]a^2=b^2+c^2[/tex]
[tex]5^2=4^2+3^2[/tex]
[tex]25=16+9[/tex]
[tex]25=25[/tex]
We can conclude that their triangle es indeed a right triangle.
